You explicitly configure the cache, as laid out here: https://bcachefs.org/Caching/

In the common case that you mentioned, data present on the full SSD would be overwritten "in standard LRU fashion"; meaning the "Least Recently Used" data would no longer be cached. New data would be written to the SSD while a background "rebalance thread" would copy that data to the HDD. I assume that the "sync" command would wait for the "rebalance thread" to finish, though I will admit my own ignorance on that front.